Brush outsides of pepper halves with oil. Place, cut-sides up, on baking sheet. Brush insides of peppers with barbecue sauce. Place, cut-sides down, on grill preheated to medium-high. Cook 4 to 5 min., or until lightly charred and slightly softened. Remove from grill. Place a cheese slice inside each pepper half, pressing cheese against to sides. Crack an egg into each pepper cup. Season with salt and pepper.
Reduce heat to medium. Place peppers back on grill over indirect heat. Close barbecue lid. Cook 15 to 20 min., or until whites are just set and yolks are still soft, or to desired doneness. Sprinkle with cilantro to serve.
For oven version, broil both sides of peppers, then fill and bake in 350˚F (180˚C) oven.
Served with grilled toast.